Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D53⋊M64 | C2 | semidirect |
| 2. #20289831 | C2 | semidirect |
| 3. #20289830 | C2 | semidirect |
| 6. #16811555 | C22 | semidirect |
| 130. D53 | #1400 | semidirect |
| 143. C53 | C2×#1400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| #20289831 | 2 |
| #20289830 | 2 |
| C2×M32×D53 | 2 |
| C2×#1400 | 53 |